相关论文: Note on the descriptions of the Euler-Poisson equa…
Euler systems are certain compatible families of cohomology classes, which play a key role in studying the arithmetic of Galois representations. We briefly survey the known Euler systems, and recall a standard conjecture of Perrin-Riou…
We construct stationary axisymmetric solutions of the Euler-Poisson equations, which govern the internal structure of polytropic gaseous stars, with small constant angular velocity when the adiabatic exponent $\gamma$ belongs to…
With the discovery of hundreds of exoplanets and a potentially huge number of Earth-like planets waiting to be discovered, the conditions for their habitability have become a focal point in exoplanetary research. The classical picture of…
The oscillation modes of stars play an important role in observations, and on the understanding of stellar stability properties. The role of viscosity in the oscillation modes of compact stars has been so far understood very loosely only,…
We present an analytic formalism that describes the evolution of the stellar, gas, and metal content of galaxies. It is based on the idea, inspired by hydrodynamic simulations, that galaxies live in a slowly-evolving equilibrium between…
Master character of the multidimensional homogeneous Euler equation is discussed. It is shown that under restrictions to the lower dimensions certain subclasses of its solutions provide us with the solutions of various hydrodynamic type…
We study adiabatic oscillations of rotating self-gravitating gaseous stars in mathematically rigorous manner. The internal motion of the star is supposed to be governed by the Euler-Poisson equations with rotation of constant angular…
The theory of stellar evolution plays a central role in astrophysics as stellar models are used to infer properties for Galactic and Extragalactic stellar populations as well as exoplanetary systems. However, despite decades of experience,…
Results from recent space missions, in particular Spitzer and Herschel, have lead to significant progress in our understanding of the formation and transport of water from clouds to disks, planetesimals, and planets. In this review, we…
The present paper is focused on the analysis of the one-dimensional relativistic gas dynamics equations. The studied equations are considered in Lagrangian description, making it possible to find a Lagrangian such that the relativistic gas…
The fates of planetary systems provide unassailable insights into their formation and represent rich cross-disciplinary dynamical laboratories. Mounting observations of post-main-sequence planetary systems necessitate a complementary level…
For the non-rotating gaseous stars modeled by the compressible Euler-Poisson system with general pressure law, Lin and Zeng [18] proved a turning point principle, which gives the sharp linear stability/instability criteria for the…
We solve Einstein's field equations coupled to relativistic hydrodynamics in full 3+1 general relativity to evolve astrophysical systems characterized by strong gravitational fields. We model rotating, collapsing and binary stars by…
We review the general theoretical concepts and observational constraints on the distribution and evolution of water vapor and ice in protoplanetary disks, with a focus on the Solar System. Water is expected to freeze out at distances…
Some cosmological models based on the gravitational theory $f(R) = R+\zeta R^2$, and on fluids obeying to the equations of state of Redlich-Kwong, Berthelot, and Dieterici are proposed for describing smooth transitions between different…
We propose in this work new systems of equations which we call $p$-Euler equations and $p$-Navier-Stokes equations. $p$-Euler equations are derived as the Euler-Lagrange equations for the action represented by the Benamou-Brenier…
We consider the dynamics of rotationally supported thin galactic disc composed of stars and gas under the influence of external tidal field and derive the coupled differential equations governing the evolution of instabilities. Further…
The Euler-Poisson (EP) system describes the dynamic behavior of many important physical flows. In this work, a Riccati system that governs two-dimensional EP equations is studied. The evolution of divergence is governed by the Riccati type…
We consider a star as a compressible fluid subject to gravitational and magnetic forces. This leads to an Euler-Poisson system coupled to a magnetic field, which may be regarded as an MHD model together with gravity. The star executes…
This review discusses (i) dynamical methods for determining the masses of Galactic and extragalactic star clusters, (ii) dynamical processes and their time-scales for the evolution of clusters, including evaporation, mass segregation, core…